The B-Spline implementation has been chosen, over the pp-spline, since it permits the direct combination of the basis functions \(B_s\)  for the spline and \(B_p\)  for the periodic portions, into one consistent set of matrix equations. In this manner the method of variable projection [1]}, [2]} can be applied, during the optimization, to separate the nonlinear from the linear portion of the computation. This improves the stability of the optimization process and reduces the computational complexity. The possibility of a piecewise continuous background \(d(t)\) , extends greatly the areas where this methods can be applied in the analysis of measurement signals.
The four parameter model [3]}, considered in the previous paper [4]}, is now a special case also covered by the model proposed here.
